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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 6, Pages 936–950
DOI: https://doi.org/10.31857/S0044466921030030 (Mi zvmmf11250) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Partial Differential Equations

Justification of the collocation method for an integral equation of the exterior Dirichlet problem for the Laplace equation

M. N. Bakhshaliyeva, E. H. Khalilov

Azerbaijan State Oil and Industry University, AZ 1010, Baku, Azerbaijan
Citations (7)
DOI: https://doi.org/10.31857/S0044466921030030
Abstract: A curvilinear integral equation of the exterior Dirichlet boundary value problem for the Laplace equation is considered. A new method is proposed to construct a quadrature formula for a singular integral. The method is used to derive a quadrature formula for the normal derivative of the double layer logarithmic potential. For specifically chosen control points, the equation is replaced by a system of algebraic equations, and the existence and uniqueness of a solution of this system are established. The convergence of the solution of this system to the exact solution of the integral equation is proved, and the rate of convergence of the method is deduced.
Key words: curvilinear singular integral, collocation method, Dirichlet boundary value problem, Laplace equation, method of boundary integral equations.
Received: 07.05.2020
Revised: 18.08.2020
Accepted: 18.11.2020
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 6, Pages 923–937
DOI: https://doi.org/10.1134/S0965542521030039
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
Citation: M. N. Bakhshaliyeva, E. H. Khalilov, “Justification of the collocation method for an integral equation of the exterior Dirichlet problem for the Laplace equation”, Zh. Vychisl. Mat. Mat. Fiz., 61:6 (2021), 936–950; Comput. Math. Math. Phys., 61:6 (2021), 923–937
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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